Interaction of Multiple Gas Jets Horizontally Injected into a Vertical Water Stream

Flow, Turbulence and Combustion 66: 183–208, 2001.© 2001 Kluwer Academic Publishers. Printed in the Netherlands.

183

Interaction of Multiple Gas Jets HorizontallyInjected into a Vertical Water Stream

OLIVIER VIGNEAU, STÉPHANE PIGNOUX, JEAN-LOUIS CARREAU andFRANCIS ROGER�

Laboratoire de Combustion et de Détonique, CNRS UPR 9028, ENSMA BP 40109,86061 Futuroscope Chasseneuil Cedex, France

Received 6 July 1999; accepted in revised form 16 April 2001

Abstract. A gas jet injected horizontally into a descending vertical water flow has two stable statescorresponding to the presence or absence of a gas pocket on the injection wall. Injecting multipleparallel jets gives rise to complex interactions dominated by two phenomena: the presence or absenceof a gas pocket and the periodic movements of the jets. The very low frequency of these movements(approx. 1 Hz) is essentially correlated with crossflow velocity and jet spacing. Different types ofinteraction were observed over a wide range of experimental conditions. In particular, a zone ofinterdependence was evidenced where interaction between jets leads to the coexistence of jets withand without a gas pocket. The influence of different experimental parameters was defined. A betterunderstanding of the mechanism of jet interaction is obtained, especially the conditions of movementof vortices and the significance of the water flow confined between the jets which modifies their meandimensions (20 to 40% increase in length and height, decrease of width without coalescence).

Key words: crossflow, interaction, multiple jets, two-phase flow.

Nomenclature

A = jet transverse section of a single jet at the abscissa x, m2

Ap = jet transverse section of a single jet for x = xp , m2

d0 = orifice diameter, mf = frequency, s−1

g = acceleration of gravity, m s−2

L = connection length for two adjacent jets in a medium at rest [22], ml = transverse characteristic dimension of a single jet at the abscissa x, mlp = transverse characteristic dimension of a single jet for x = xp , ml0 = distance between injection holes, mm0 = mass flux of injected gas, kg s−1

N = number of jetsP = value of a pixel on a binarised image (1 or 0)Qa = suction rate per side, m3 h−1

Ql = liquid flow rate, m3 h−1

r2 = correlation coefficientu′, v′, w′ = velocity fluctuations (r.m.s.) along x, y and z axis, respectively, m s−1

� Author for correspondence.

184 O. VIGNEAU ET AL.

Ul = mean transverse flow velocity for x = 0, m s−1

Ulp = mean transverse flow velocity for x = xp , m s−1

w = mean velocity component associated to the Oz axis, m s−1

Wg0 = mean velocity of gas injected, m s−1

x, y, z = Cartesian coordinates, mxp = length of the gas pocket, m

Greek Lettersδ = boundary layer thickness, mδy = width of the jet, mδz = height of the jet, m∇2h = Laplacian of the function, hµg0 = gas viscosity at injection, Pa sµl = liquid viscosity, Pa sρge = gas density in the test section, kg m−3

ρg0 = gas density in the injection plane, kg m−3

ρl = liquid density, kg m−3

Dimensionless numbersCs = suction rate per side = 4Qa/Ql

Fr = Froude number based on the length of the gas pocket = Ulp/√gxp

Rv = injected and main flow velocity ratio = Wg0/Ul

Re0 = Reynolds number at the injector = (ρg0Wg0d0)/µg0Reδ = Reynolds number based on the boundary layer thickness = (ρlUlδ)/µl

St = Strouhal number based on the length of the gas pocket = f xp/Ulp

StL = Strouhal number based on the length of connection for two adjacent jets= fL/Wg0 [22]

Tu = turbulence rate =√(u′2 + v′2 + w′2)/3U2

l

$d = jet spacing to diameter ratio = l0/d0$j = jet-to-mainstream momentum flux ratio = (ρg0W

2g0)/(ρlU

2l )

$p = jet spacing to characteristic single jet size ratio = l0/lp$v = gas pocket feeding to emptying velocity ratio = m0/(ρgeUlpx

2p)

Indices0 = injectorc = criticalg = gasl = liquidp = end of the gas pocket

1. Introduction

The literature on jets submerged in a crossflow is abundant, which is understand-able given the theoretical significance of the subject and the diversity of industrialsituations involved. This type of flow is of theoretical interest because it combinestwo fundamental situations in fluid mechanics: flow on a wall and a jet developing

INTERACTION OF MULTIPLE GAS JETS 185

Figure 1. Missile scale model [11].

in a medium at rest. The most common applications are in the field of verticaltake-off aircraft, the cooling of turbine blades by a cold air film, fluid mixing inchemical reactors and combustion chambers and the dispersal of industrial pol-lutants in rivers or the atmosphere. This is why there have been so many studiespublished on cases where the two fluids that make up the jet and the crossflow havedensities of the same order of magnitude.


The same type of flow, but in a two-phase configuration, is encountered duringthe launching of a missile from a submarine. As it gets closer to the surface ofthe sea, the decrease of pressure makes it necessary to evacuate the air from theinterior: gas jets also develop on the surface of the missile, as presented in Fig-ure 1. Interaction can be very significant on the behaviour and the trajectory of themissile.

The objective of this study is also to present the set of phenomena observedwhen multiple horizontal gaseous jets are injected in parallel into a vertical liquidflow and to describe the influence of the main parameters on the shape of the jetsobtained. Two quite different solutions can be advanced and sometimes co-existdepending on the experimental set-up: jets with a significant gas pocket and thosewithout (both described in Section 3). Moreover, various types of instability areencountered.

As far as we know, it does not exist any exhaustive study of gas jets injectedinto a liquid crossflow in a similar configuration. Consequently, we present themain results concerning the interaction between multiple jets injected in parallelinto a crossflow of similar density that help to understand the following results.

Generally speaking, a jet injected at the centre of a row can be considered ashaving the same shape as a single jet, even if the former is narrower and thicker thanthe latter. Nevertheless, Sugiyama and Usami [19] note that the flow generated bymultiple jets in a crossflow cannot be reconstructed by superimposing flows froman isolated jet. The coherent structures that exist in a homogeneous jet subjected tocrossflow (horseshoe, ring, contrarotating and wake vortices), amply described byFric and Roshko [5, 6] can be modified according to the interactions between jets.

The main variables necessary to understand the phenomenon are (i) the jet-tomainstream momentum flux ratio $j , equal to the square of the velocity ratio Rv

if the densities of the fluids used are equal (Holdeman and Walker [8] consider that$j is the most significant independent variable influencing both penetration andmixing), (ii) the number N of orifices (Gregoric et al. [7] show that the expansionof jets increases and their thickness decreases as the number of jets decreases),(iii) the geometrical parameters (diameter d0 of the injectors and the space l0between them).

The influence of numerous variables is the source of the complex couplingsencountered. Savory and Toy [18] note that certain parameters need to be handledwith care, especially the space l0 between the jets – the situation of widely spacedjets (behaving like single jets) and that of closely spaced jets (with very weakpenetration of the transverse flow between the jets) are fundamentally different.Finally, Gregoric et al. [7] are the only authors to propose jet geometry correlation(penetration and normalised area) in terms of experimental parameters. Penetrationvalid for a ratio Rv of between 1 and 5, for a number of jets between 1 and 7 andfor reduced abscissas x/d0 less than 100 is expressed as

z

d0= 0.78R0.93

v N−0.17

(x

d0

)0.52

. (1)


Figure 2. Diagram of a jet injected downwards into a left-to-right liquid crossflow; $j = 1,Re0 = 25,000 [14].

It is to be noted that the spacing between jets does not appear in this equation.In the case of homogeneous jets, the phenomena are then complex due to the

great number of parameters involved and to their mutual interactions. Moreover,as gas jets are injected into a vertical water flow, additional phenomena linked tothe great difference of densities and/or to the gravity may strongly modify thosepreviously described. The surface tension of the liquid seems to be of secondaryimportance even if it necessarily plays a role in the mixing of the two phases. Forexample, a sonic gas jet submerged in a liquid at rest, dividing by two the surfacetension leads to a variation of 15% for the entrained surrounding liquid and of afew degrees for jet angle (i.e. the angle subtended by the cone representative of thejet shape) [12]. Moreover, experiments involving vertical downward injection of airinto a horizontal water current with jet to mainstream momentum flux ratio values$j ≥ 1 and Re0 values ≥ 25,000 leads to two-phase jets, as shown in Figure 2,of exactly the same type as homogeneous jets and, more particularly, to two flowsthat are completely separate far from the injector [14].

After describing the experimental set-up, results for gas jets in a vertical down-ward water stream are presented, underlining the existence of two different solu-tions for the jet, depending upon whether or not a stable gas pocket appears. Theconditions under which they exist will be defined. This will be followed by apresentation of the complex instabilities generated by jet interaction, leading toquite different physical phenomena. The periodic, very low frequency movementgenerated by these instabilities will then be studied. Finally, the influence of the


Figure 3. Experimental set-up.

principal experimental parameters will be brought to light as independently aspossible of their couplings.

2. Experimental Set-Up

The test bench is presented in Figure 3. The water flow, whose temperature alwaysstays close to 25◦, is generated by a 30 kW pump connected to two 3 m3 tanks inorder to eliminate any air bubbles circulating within the water downstream of thegas injection. The water is fed into a 4 m high vertical pipe through a magneticflowmeter, then it travels through two wide radius elbows, two grids with 5 mmmesh, a 1.6 m pipe, a hexagonal honeycomb net (6 mm mesh, 80 mm high, 2.5%blockage of the section) followed by a straight convergent nozzle with a circularentrance and a square exit and a contraction rate of 1.6, with a maximum angle of 5◦and length 0.32 m. LDV measurements showed that the accuracy on the volumetricflow rate of the liquid is 2.5%. The flow then crosses the suction device from top to


Figure 4. (a) Convergent nozzle, (b) suction device, (c) test section.

bottom which makes it possible to vary the main flow boundary layer. It then goesthrough the test section where the jet is formed and returns to the tanks.

The suction device – which makes it possible to diminish the thickness of theboundary layer and the rate of flow turbulence near the wall – shown in Figure 4band described in [20], is a 0.135×0.135 m2 square pipe, 0.25 m high. To achieve agreat variation in its thickness, a rectangular slot was made 0.15 m upstream of gasinjection on the main and lateral faces of the water piping. Vigneau [20] has shownthat this distance is sufficient for flow to be reestablished after suction. The planefacing the injector is left free for carrying out velocity measurements (this slight


asymmetry in flow has no influence on the jet’s development). The 0.13 × 0.02 m2

slots are inclined at an angle of 45◦ and their upper end is profiled for easier waterevacuation. This layout avoids vortices appearing in the exit pipes. The slots arewide so as to avoid excessive velocity of suction flow as shown in Figure 4b.

The test section, represented in Figure 4c, is a 0.135 × 0.135 m2 vertical squarepipe, 0.7 m in height, with three glass walls and one stainless steel wall throughwhich the jets are injected. The injection plane boundary layer follows a flat-platetype law, and its thickness can vary from 25 to 8 mm with suction rate Cs . Thethickness δ is calculated using the displacement thickness: in a confined flow, thismethod provides a more accurate value of δ than the classical thickness criterionwhere the velocity is equal to 99% of exterior velocity. Vigneau et al. [21] haveshown that boundary layer thickness δ obeys the law given in Equation (2), whereδ0 is the thickness of the boundary layer in the absence of suction. This drop iscoupled with a drop in turbulent energy close to the wall.

δ

δ0= e−6.28Cs . (2)

All the trials were carried out with a Cs value equal to 0.08, i.e. with a boundarylayer about 10 mm thick. In these conditions, the Reynolds number Reδ (associatedwith the boundary layer thickness) varies between 13,000 and 40,000. Since theturbulence rate Tu at the centre of the liquid flow upstream of the injector’s positionstays close to 1%, the laminar/turbulent transition for the Reδ given by Cousteix[3] completes between 5,000 and 6,000. Consequently, the liquid flow near the gasinjection always remains fully turbulent.

Air is supplied by a 10 bar compressor into a large pressurised tank beforepassing through a sonic nozzle making it possible to calculate the mass flow rate.An injection system made up of a 20 × 20 × 76 mm3 chamber and a plate withcircular injectors is fed via three parallel tubes to ensure good quality flow. Up-stream of each injector, the gas passes through a conic contraction nozzle whosecontraction rate is equal or greater than 20, depending on the injectors’ diameter.These diameters are equal to 0.5, 0.7 or 1 mm and associated length over diameterratio is in the range [1.4, 1.6] (slug-flow type). The measured gas flow is veryclose to the theoretical one, and the Reynolds number associated with the inject-ors’ diameter varies between 3,700 and 30,000. Such a system enables variation ofinjection characteristics (see Table I for the number of jets, diameter and spacing),over a surface of 20 × 76 mm2.

Void fractions were measured using an Optoflow optical probe, described indetail by Pignoux [16]. Visualisation was carried out from front and side using anHi8 video Camera (769×574 pixels) with the jet illuminated by two 500 W halogenspotlights. The diffusion of light through a gas liquid interface makes it especiallyluminous. 3,000 images were obtained at a rate of 25 per second and at a shutterspeed of 1/6000th. Processing is carried out using Optimas software which adaptsdefinition to the camera used. Under the conditions of this experiment, a pixel


Figure 5. Representation of distribution of pixels for a portion of image [16].

corresponds to a 0.8×0.8 mm2 square. Thirty-two uncorrelated images – sufficientto obtain a representative average of the phenomenon [16] – are extracted from thefilm and transformed into 256 levels of grey and binarised with a threshold fixed bythe operator. The image thus has two colours – white when the light is diffused bythe jet and black for the background. Finally, the contour of the jet correspondingto colour change is extracted using the two-dimensional Laplacian operator. Forexample, for a portion of image 3 × 3 pixels (Figure 5), the value of the Laplacianapplied to the central pixel is approached by Equation (3).

∇2h = 4P5 − (P2 + P4 + P6 + P8). (3)

Pignoux [16] has shown that the results obtained were reproducible and that thejet edges were within a mean width span of 2.5 mm (3 pixels).

3. Presentation of Gas Jets in a Vertical Water Stream

The lack of literature on gas jets in liquid crossflows has already been mentioned –only Dawleh [4], Pignoux [16] and Vigneau [20] have given precise descriptions oftheir structure. A gas jet horizontally injected close to the wall veers sharply underthe influence of the liquid flow. The structure of the jet can be divided into threezones shown in Figure 6, the separations between them can be highly intermittent.The first one corresponds to a stable gas pocket in equilibrium close to the walland surrounded by a turbulent gas-liquid interface. The second is made up of avortical structure, which generates the mixture between phases. Finally, the thirdcorresponds to the jet’s loss of cohesion downstream of the vortical structure – theliquid flow entrains the gas-liquid mix in an disorderly fashion. This type of jetis characterised by gas pocket stability and the rigidity of the interface betweengas and liquid. Unlike the classical jet in a crossflow [5, 6, 15], the contrarotativevortices are not observed [21].

The acceleration of gravity, the velocity and density of the liquid, the velocityand density of the gas at the injection, the density of the gas in the test section [11],the diameter of the injector and the axial length are the factors liable to intervenein the structure of the resulting gas-liquid flow.� For example, in zone (1) of the jet,

� The surface tension seems to have a slight influence (see Section 1).


Figure 6. Structure of a gas jet horizontally injected into a liquid crossflow.

the thickness of the gas pocket δz, on the injector’s plane xOz, defined in Figure 6and measured according to the method laid out in Section 2, depends strongly onaxial distance, liquid velocity, gas mass flow and very weakly on injector diameter[4].

All studies undertaken [4, 16, 20] show that it is overall gas flow that intervenesin the equations and not injection velocity, injected gas density or injection dia-meter taken separately. The lack of influence of the injector’s diameter specificto this configuration is of importance as it makes difficult to use the classicaldimensionless numbers.

The thickness of the gas pocket is not representative of the three-dimensionalcharacter of the first zone of the jet. It is more able to define a characteristictransverse length, a geometric average of its height and semi-width and thus rep-


resentative of its section which is assimilated to a semi-ellipse (cf. Figure 8a). Thedimensional analysis of the function

l =√

2A

π=√δyδz

2= f (x, ρl, Ul,m0, g, ρge),

proposed by Pignoux et al. [17], is represented in Equation (4).

l

x∝(

m0

ρgeUlx2

)α (Ul√gx

)β (ρl

ρge

)γ

. (4)

The gas pocket can be assimilated to a stable bubble fed from above by the injectedgas and emptied below by movement of the liquid [17]. It is most likely the seatof a longitudinal recirculation as shown numerically by Magnaudet et al. [13] inthe case of a two-dimensional jet. The section of the jet increases with x, thus thevelocity of the gas in the pocket diminishes. For x = xp, the latter becomes tooweak and the liquid then entrains the gas which does not circulate upstream towardsthe main vortex (2). Downstream of the main vortex, the jet loses its cohesion andthe gas is evacuated by packets. As the gas pocket is the element which managesthe first part of the flow, its length xp (cf. Figure 6) is the obvious candidate forcharacteristic axial length.

The length was measured with a mean relative error close to ±5% by Pignoux[16] using the following method: a slice of light in the gas flow is obtained using alaser beam via a top-hat lens which ensures constant lighting over the whole of thefilmed zone. The length of the pocket is obtained from an average of the imagesobtained with a camera CCD and processed using Optimas software. Equation (4)is then transformed into Equation (5); as the ρl/ρge did not vary during this work,it was integrated into the proportionality constant. Finally, the velocity of the liquidis determined for x = xp, which make it possible to take the confinement of theliquid by the gas pocket into account.

l

xp∝(

x

xp

)1−2α−β/2(

m0

ρgeUlpx2p

)α (Ulp√gxp

)β

=(

x

xp

)1−2α−β/2

$vα Frβ. (5)

As xp is a unknown variable that depends on factors already mentioned (velocityof the liquid, gas flow, etc.) as well as other uncontrolled factors, the analysis ofassociated dimensionless numbers thus is an operation which more delicate thanif one were dealing with an independent factor. The ratio m0/ρgex

2p represents the

gas flow feeding the pocket normalised by x2p, a magnitude linked to the gas-liquid

interface. The ratio $v thus represents the ratio of the velocity of the gas feedingthe pocket to that of the liquid emptying it. One also observes the appearance of theFroude number with respect to the length of the pocket, i.e. the ratio of the forcesof inertia and buoyancy, representative of the stability of the gas-liquid system.

On the other hand, experimental results show that the transition between zones(1) and (2) in Figure 6 (thus x = xp) takes place when Equation (6) is verified

$v = 0.035Fr−2.7, r2 = 0.84. (6)


Figure 7. Evolution of the characteristic transverse dimension for x = xp .

Using Equations (5) and (6) it is possible to determine the jet’s correspondingcharacteristic length lp at this position (Equation (7) and Figure 7).

lp

xp= 9.6$v0.64, r2 = 0.95. (7)

However, former studies only concern jets with stable gas pockets. The studyof the interaction of multiple jets entails wide variation in liquid velocity and gasflow, and the existence of gas jets without pockets shows up when liquid velocity ishigh. In this case, the gas issuing from the injector is deflected by the liquid to suchan extent that the gas pocket is unable to take on a stable shape. This suppressesthe first two zones described in the gas pocket case as the gas is highly diluted bythe liquid stream as soon as it leaves the injector and is thus evacuated. The jet thentakes on the form of a mixing of gas and liquid.

Figure 8 gives the comparison between iso-void fractions plots for several sec-tions of a pocketless jet and sections of jets with pockets, the latter sections beingextrapolated on the basis of the results of Pignoux [16] (as they cannot be ob-served experimentally). The phases are much better mixed and the size of the jet issignificantly lower in the absence of a gas pocket.

For numbers $v < 0.04 corresponding to high rates of liquid flow or low gasflow, Equation (7), can be approximated by relation (8):

lp

xp= 3.7

√$v ⇒ lp = 3.7

√m0

ρgeUlp

; (8)

the value of the coefficient can depend on other parameters such as density andsurface tension of the liquid or the ‘quality’ of exterior flow such as the thicknessof the boundary layer of the liquid. When the characteristic length lp , upper-boundof l, becomes too weak, axial recirculation can no longer take place and, undersuch conditions a pocket cannot appear. The liquid penetrates the jet almost im-mediately. The transfer of momentum flux between the liquid and the gas then


d0 = 1 mm, m0 = 0.166 g s−1, Ul = 5.6 m s−1

(a) jet with gas pocket, extrapolated from [16] (b) jet without gas pocket, real case

Figure 8. Void fraction distributions for a jet with a pocket (extrapolated from [16]) andwithout one (measured); Re0 = 12,000, Reδ = 63,000.

occurs rapidly, the liquid being first entrained by the gas and then vice versa, thegas by the liquid. As exterior liquid velocity increases, the jet loses its pocket;however, if at the same time, boundary layer thickness of the liquid is sufficientlyreduced, the pocket will reappear. A simple intuitive argument would have led toan opposite conclusion.� However, the decrease of the boundary layer thickness iscoupled with a decrease of the turbulent kinetic energy close to the wall; the higherthe turbulence in this region, the easier the jet will lose its pocket. Moreover, thisobservation is in accordance with that of Chang and Vakili [1].

� When δ is low, liquid velocity near the wall is high, which means that the liquid should havebeen more susceptible to penetrate the jet.


(a)

(b)

Figure 9. Sites of two phase jets in a crossflow.

Sites where jets with and without pockets exist are given in Figure 9. Figure 9awas plotted using experimental points bringing together tests with single or mul-tiple jets in diverse interaction domains (cf. Section 4). In the multiple jet case, thenumber of jets and their spacing have no influence on the existence of at least onepocket, as jets with or without pockets can co-exist. Figure 9b shows the influenceof the boundary layer thickness on the destruction of a gas pocket. In that figure,the drawn curves show a schematic partition between different regions where thegas pocket is present or not. It will be shown below that the loss of coherence ofa jet in a row is due to its interaction with the others. Figure 9 thus represents amultiple jet case with or without a pocket for at least one jet in the row.

The previous figures and Equations (7) and (8) give a very general definitionof the shapes of single or multiple jets in terms of experimental parameters. In-teraction between jets corresponding to the ‘jets with pockets’ zone is discussedbelow.


Table I. Multiple jet injection conditions.

N 1 2 2 2 2 2 3 3 3 3 3 4 5

d0 (mm) 0.5 0.5 0.5 0.7 1.0 1.0 0.5 0.5 0.7 0.7 1.0 0.5 0.5

l0/d0 – 12.5 50.0 25.0 12.5 50.0 12.5 25.0 12.5 25.0 12.5 12.5 12.5

4. Jets Interaction

As this study covers a wide field, diverse forms of interaction were encountered.At least eight main variables are involved: number, diameter and spacing of jets,boundary layer thickness, liquid velocity, gas flow, gas and liquid densities. Theconfigurations given in Table I were used in this study.

For the experiments carried out, the mean rate of obstruction, calculated fromthe sum of the sections of single jets, is close to 17%. It constitutes an upper-boundof real obstruction as interactions between jets diminish the section occupied by gaspockets. In particular, in the least favourable case, the distance from the jet edge tothat of the test section is equal to 15–20 mm. It is to note that the obstruction doesnot seem to play a significant role in the mechanism of the jets interaction.

The main parameter used here is the $p ratio, defined in Equation (9) as theratio of space l0 between the jets and the characteristic dimension lp of a single jetunder the same conditions.

$p = l0

lp. (9)

The set of phenomena discussed below was studied for experimental conditionssituated within the domain of jets with pocket in Figure 9.

4.1. ISOLATED JETS

These jets are defined as showing all the characteristics of single jets under identicalconditions without interaction.� In the jets with pockets, the associated vorticalzones are independent with adjacent jets (cf. next section). This case was nottotally observed owing to the geometric limitations of the test section. It would,however, seem that this situation cannot hold for $p values lesser than 3.5. Indeedthe situation of $p = 3 was studied and displays differences of less than 10% withthe shape of a single jet. This case was also not strictly a separated jets one, but itshowed that the value of 3.5 proposed previously was reasonable.

� Another definition of isolated jets could have been jets with non-correlated vortical zones andwith their axes strictly parallel to the direction of the crossflow. However, this definition would notbe useful for the case of the circular geometry (as for the case of the missile presented in Section 1),where the jet axes do not move because the system is closed.


Figure 10. Weakly interacting separate jets; vortices’ periodic movement.

4.2. SEPARATE, WEAKLY INTERACTING JETS

This type of interaction corresponds to jets separated by the water flow, with char-acteristics similar to those of isolated jets but whose vortices have a downwardperiodic movement in opposite phase to adjacent jets. Figure 10 shows this phe-nomenon for a two jets case. This corresponds to $p values of between 1.7 and 3.5.Alternating vortices constitute a regular, periodic very low frequency phenomenon(of the order of 1 Hz). These frequencies are studied in Section 5.

4.3. SEPARATE, STRONGLY INTERACTING JETS

These jets are sufficiently far apart to each have their own gas pocket, but notenough to develop completely symmetrically with respect to their injection posi-tion. The jets repel one another and the centreplanes of the lateral jets are deflectedin the direction of the liquid stream. This is characteristic of two-phase jets – therigidity of the gas-liquid interface prevents the jets from coalescing as is observedfor homogeneous jets [2, 9, 10, 18].

The study of the distribution of void fractions for several transverse sections ofthe jets shows that the jets are totally separate (although deflected) up to a distanceof several tens of diameters.

This kind of interaction is observed for values of $p that depend on the numberof jets since the less they are, the easier they repel one another, the lateral jetsconfining the central ones. The separation between strong interaction and the in-terdependence described below depends solely on N and corresponds roughly to acritical value $pc, given by Equation (10).

$pc ≈ 0.2N. (10)


N = 2, d0 = 1 mm, l0 = 50 mm, m0 = 0.184 g s−1, Ul = 1.1 m s−1

(a) t (b) t + T/4 (c) t + T/2

Figure 11. Separate jets with strong interaction: alternating vortices coupled with widthfluctuations; Re0 = 14,000, Reδ = 12,000, $p = 1.1, Fr = 1.7.

In the case N is too high (typically above 5), the row of jets shifts to the situationof interdependence described below, with no intermediate domain where the twotypes coexist (no case of a row of jets strongly interacting at the exterior anddependent towards the centre has been observed).

Alternating vortices, similar to weakly interacting jets are also a fundamentalaspect of this situation. Moreover, the width of the jets is linked to this alternation– the interface line that separates the jets fluctuates in rhythm with the vortices.Visualisations of this phenomenon are given in Figure 11.

4.4. INTERDEPENDENT JETS

This is a more complex case. To put matters simply, it is more often found whenjets are numerous enough (confinement between jets is too great for the jet’s axisto be deflected) and sufficiently close to keep $p < $pc. One or more jets willhave pockets while the others develop like pocketless jets. This is a highly unstablesituation, and the pockets can appear and disappear, their number can increaseor decrease unpredictably. This phenomenon is shown in Figure 12 for varying


Figure 12. Variation in number of pockets with Reδ ; Re0 = 3,700.

Reδ with fixed gas flow, jet number and spacing. The liquid velocity axis thuscorresponds to a vertical straight line on the plane in Figure 9a.

Jets with a pocket show very low frequency, periodic movements of the sametype as those described for weak or strong interaction. Visualisations of interde-pendent jets are given in Figure 13 for three jets with two pockets. These aremoving as if they belonged to two separate jets in strong interaction; the pocketlessjets do not perturb this phenomenon and it will be seen below that they do notchange its frequency.

The jets in weak or strong interaction do not mix with each other and repel,the gas-liquid interfaces behaving like ‘supple walls’. These interactions producesmall angle deviations of the axes of the jets. The situation of interdependence canthen be considered as a situation where jets influence each other strongly, a centraljet pushing its neighbours sufficiently to make the deviation angles become greaterthan a critical angle. This phenomenon leads to the destruction of one or severalpockets, permanently or not, instead of any form of coalescence. The values of theangles, approximately a few degrees, are difficult to measure and consequently itwas not possible to define a critical value of this angle. The mechanism of interac-tion leading to the situation of interdependence is thus difficult to describe, but itseems that a central jet too confined by its neighbour rises lightly, as shown on thevoid fraction distribution in a transverse section given in Figure 14.

The water confined between the jets could be the origin of this rising whilepassing under the central jet and suppressing the stabilisation effect of the wall onthe gas pocket, leading in certain cases to the destruction of this pocket.

When injectors are very close to one another (space l0 slightly larger than dia-meter d0), different phenomena to those described above appear, probably becausethe liquid does not pass between the injectors. Two solutions can be considered inthis case: the jets can be too close to possess one or several pockets, or they coalesce


N = 3, d0 = 1 mm, l0 = 12.5 mm, m0 = 0.137 g s−1, Ul = 1.5 m s−1

Figure 13. Interdependent jets displaying a movement of two vortices of the strong interactiontype; Re0 = 9,900, Reδ = 17,000, $p = 0.37, Fr = 1.9.

Figure 14. Distribution of the void fraction for the case of rising of the pocket of a central jetin a situation of interdependence; Re0 = 6,900, Reδ = 43,600, $p = 0.55, Fr = 3.8.


Figure 15. Areas of existence of the different kinds of interaction.

to create a unique pocket. This configuration has not been dealt with in this work,but it was necessary to note it in order to complete the proposed classification.

Parallel injection of multiple gas jets into a liquid crossflow gives rise to com-plex interaction phenomena that can be grouped into four types: separate jets,(weakly or strongly) interacting jets, interdependent jets and close jets. The ra-tio $p makes it possible to define the existence zones of the types as shown inFigure 15.

The influence of experimental parameters on the shape of the jets is studied inSection 6. In the case of interacting and interdependent jets, low frequency, periodicmovements show up. These are studied in the following section where it is shownhow they can provide the bases necessary to understanding the physical mechanisminvolved.

5. Low Frequency, Periodic Movements

To determine the frequency of the vortex movements discussed above, visual-isations were carried out for all the spacings, diameters and numbers of orificespresented in Section 2. In each of these configurations the only water and gas flowsused were those where jets were in weak or strong interaction; interdependentjets were treated separately. When two-phase vortices diffuse light, they becomevery luminous, making it possible to measure the frequency of their movements.A phototransistor placed facing the images at the fluctuation boundary of a vortexsuccessively receives a very luminous signal (vortex high) or a not very luminoussignal (vortex low). The signal is integrated, then recorded on a digital oscilloscope(500 points at a frequency of 25 Hz). The spectrum of the signal is obtained byFast Fourier Transform (FFT). As the frequencies of the movements are of theorder of 1 Hz, the video frequencies used are greater (25 Hz) and do not disturbmeasurement. A typical example of a signal and spectrum is given in Figure 16.

For weak and strong interactions, the experiments show that the frequency de-pends strongly on liquid velocity and jet spacing, weakly on gas flow and never ondiameter of the holes nor number of jets.

This result is also valid in the case of interdependent jets when a periodic phe-nomenon develops. For example, in the case of three jets where the central jet hasno pocket, the frequency of the two exterior jets’ movements can be calculated


Figure 16. Signal versus time (a) and spectrum (b) allowing frequency measurements;Re0 = 23,000, Reδ = 21,000, $p = 0.80, Fr = 2.2.

using spacing equal to 2 × l0, the central jet will have no influence as long as it hasno pocket.

Although it was noticed that frequency generally increased slightly as δ in-creased. In the case of three jets with pockets, in certain cases, an increase in δ

sufficiently increases movement frequency for the central jet pocket to disappear,leaving the exterior jets to continue interacting but at a lower frequency. This in-fluence is of the same type of that destroying (or not) the gas pocket for a singlejet.

The transverse movements of groups of jets injected in a medium at rest aremore or less understood [2, 22]. For these authors, the vortical zone present inthe space between adjacent jets in a two-dimensional jets network induces andmaintains a periodic pulsation movement of these jets. In this case, the resultingfrequencies can be calculated with the Strouhal number based on the initial velocityof the jets and their connection length as follows:

StL = fL

Wg0= [0.008; 0.02]

in a medium at rest, depending on the geometry [22]. (11)


Figure 17. Vortex movement frequency St = f ($p,Fr).

As in our case, pulsation frequency rises with jet velocity but diminishes as thedistance between jets is increased.

In the configuration of our study, the vortices that interact could be the vorticalzones of the jets with pocket. These vortices are not induced as in the case ofVillermaux et al. [22]. They seem to be inherent (see Section 3) in the structureof a jet with pocket, the seat of longitudinal recirculation. In the area close to theliquid-gas interface, the gas is entrained downstream and part of it feeds the axialvortex (2) in Figure 6 and other part recirculates upstream due to the depression thatexists just downstream of the injector. The characteristic time it takes to recirculateup is very likely much longer than the time it takes to descend and this is probablywhat is responsible for the frequencies observed. Therefore, the mechanisms couldbe of a similar type and the periodic movements could be inherent in the interactionof the vortical zones of adjacent jets.

The frequency of the pocket’s movements seems to depend on its length, onliquid velocity and the acceleration of gravity. These three variables are respons-ible for a characteristic time. Moreover, as in the Villermaux et al. [22] case, thefrequency is strongly linked to mutual jet confinement. Finally, boundary layerthickness remained constant throughout the present study. Dimensional analysisof the function f = g(Ulp, g, xp, lp, l0) shows up the numbers Fr and $p previ-ously defined. Equation (12) represented in Figure 17 gives a good account of thephenomenon.

St = 9.1 × 10−3$p−0.5 Fr1.6, r2 = 0.89. (12)

For two axisymmetric jets submerged in a medium at rest with a $d = 20, forexample, and according to Villermaux et al. [22], the Strouhal number calculatedfrom the mean gas velocity between the origin and the length L varies from 0.04to 0.10. This domain is in very good agreement with the results of this study.

Measurements in the near field of the vortices would be of interest to confirmthis result but, given the three-dimensional nature of the problem, the difficulty of


Figure 18. Exterior contours for variable N ; Re0 = 7,500, Reδ = 35,000, $p ≈ 0.5,Fr ≈ 3.3.

carrying out measurements between the jets in an unstationary flow requires theimplementation of very complicated test apparatus.

6. Influence of Experimental Parameters on the Shape of the Jets

Vigneau et al. [21] noticed that the variation in boundary layer thickness of waterupstream of a single jet neither modifies its exterior shape nor its internal struc-ture. With multiple jets, even though significant instability occurs, on average thejets’ shape is not modified by suction rate. The mean sizes of the jets, i.e. theirpocket length, height and width for x = xp and their mean profiles are insensitiveto boundary layer variation, except of course when a decrease in boundary layerthickness is such that one passes from a state of strong interaction to one of inter-dependence as described above. Mean water velocity alone determines the shapeof the jets, their length and height increasing and decreasing with Ul, respectively.In the same way, growth in gas flow m0 entails growth in the length and height ofthe jets.

When comparing the development of a gas jet in a row with an isolated jet,one observes phenomena similar to those presented by Gregoric et al. [7] andHoldeman and Walker [8] for homogeneous jets. A jet in a row is narrower andhigher than a single jet. The lateral jets play a confining role whose effects aretwofold: jet width is limited by lateral confinement and crossflow is significantlyaccelerated between the jets, which also contributes to restricting their width. The$j ratio is decisive for jet evolution – as with a single jet – when it increases so thejets grow in size (i.e. height, width and length). $j should however be used withcare for reasons already given.

The reduced spacing $d cannot be used as in studies on homogeneous jetsbecause it is not significant for the two-phase jets under consideration. In Section 5,it was shown that the frequency of movements did not depend on diameter but onlyon spacing (l0). On average, high variation of $d (from 12.5 to 50) does not modifyjet profile; this result has been confirmed in all the configurations studied.


The influence of the number N of jets was studied with constant spacing forN = 1, 2, 3 and 5 jets. These cases correspond to isolated jet situations (N = 1),strongly interacting jets (N = 2 and 3) and interdependence (N = 5). Figure 18gives results for the evolution of jet height, defined in Figure 6 and measured fromvisualisations described in Section 2, which is all the greater when the numberof jets is high. It is to be noted that these results are similar to those presentedby Gregoric et al. [7] after visualisation of homogeneous jets – they obtained anincrease of about 20% between N = 1 and N = 3.

The flow studied is complex and involves a large number of variables. Theinfluence of gas and liquid flow has been shown and is similar to that observed bynumerous authors for homogeneous jets. However, contrary to the homogeneouscase, the diameter d0 is not significant. It is interesting to note that the geometricalparameters are independent (number of jets and spacing): jet penetration increaseswith N independently of l0. Such influence is the opposite of that evidenced in thestudy of the vortices movements – their frequency decreases with l0 and does notdepend on N .

To our knowledge, these results are the only ones available for this type of two-phase flow. The main difference with the homogeneous case is the non-coalescenceof the jets, the gas-liquid interface behaving somehow like a ‘supple wall’. Theconfinement of the water passing between the jets as well as the confinement dueto the adjacent jets causes them to lengthen and reduces the width of the centraljets, the lateral jets being deflected from their axis. Height increases with N , butdepends little on spacing. More work is needed to gain better insights into thephysical phenomena involved in the development of periodic movements, whichresult from the interaction between two non-induced vortices as seen in Section 5.In particular, velocity and pressure measurements in the water between the jetsare indispensable for a greater understanding of the decisive nature of this zonevis-à-vis the downstream in conformity with the results in Section 5.

7. Conclusions

The study of gas jets horizontally injected into a vertical descending water streamnecessitates taking into account two stable situations: jets with and without gaspockets. Jets with gas pockets have a very rigid gas-liquid interface, which preventstheir coalescence. The conditions under which these two cases exist have beendefined and they can coexist if the number of jets is high or if they are too closetogether. This duality leads to complex interaction phenomena, which fall into fourclasses: separate jets, (weakly or strongly) interacting jets, interdependent jets andclose-set jets (not treated here).

Jet interaction leads to very low frequency, periodic movements dependent onwater velocity, mass flow rate of the gas and distance between jets. The influenceof the thickness of the water boundary layer upstream of the jets has been shownbut not totally quantified. The law defining fluctuation frequency obtained with


interacting jets can also be used in the case of interdependent jets provided thespace between two existing jets is used. The movements find their origin in theinteraction of two vortices that are non-induced by this same interaction; thesemovements are inherent in the coexistence of the vortices. It was possible to useacceptable dimensionless numbers based on the length of the gas pocket.

The influence of experimental parameters on the average shape of the jets hasbeen studied (height and length). Water velocity and gas flow have an influencesimilar to that observed for homogeneous jets. The geometric parameters (spa-cing and number of orifices) have a different influence which clearly underlinesthe independence of the average jet shape from fluctuation frequency. The num-ber of holes influences jet penetration whereas spacing is decisive for fluctuationfrequency.

Acknowledgements

We would like to thank the Aerospatiale Society for supporting this work. Wewould also like to express special thanks to J. Baillargeat for conceiving the fre-quency measuring system.

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Interaction of Multiple Gas Jets Horizontally Injected into a Vertical Water Stream